{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 30,
  "input_formula": "N16Si12Sr2",
  "input_spacegroup": "Imm2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -228.2881069961974,
  "input_cartesian_polarization_e_A2": [
    -8.227415805183476e-18,
    3.6691041109482637e-17,
    -0.0006564528063687292
  ],
  "input_reduced_polarization": [
    -3.7256416629247826e-16,
    1.4098395246681691e-15,
    -0.04870000735998039
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Immm",
      "spacegroup_number": 71,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4669118491483384e-15,
      "parent_symmetrization_rmsd_A": 0.4331070561133806,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -213.53605977324105,
      "reduced_polarization": [
        -2.398053859093839e-15,
        3.6745172009100903e-16,
        4.471811643571084e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.295674680237815e-17,
        9.562922539558246e-18,
        6.027788212177757e-18
      ],
      "ranking_score": 0.4331070561133855
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Imm2",
      "spacegroup_number": 44,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00010076653596583094,
      "parent_symmetrization_rmsd_A": 0.003149967483966776,
      "parent_cell_rmsd_A": 0.0021364916779115393,
      "energy_eV": -228.2849939665416,
      "reduced_polarization": [
        -1.868565190067918e-15,
        -3.625202719281328e-15,
        -0.00010076653596583094
      ],
      "cartesian_polarization_e_A2": [
        -4.1246786384862087e-17,
        -9.432133585314321e-17,
        -1.3588317483075464e-06
      ],
      "ranking_score": 0.5038856234753764
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Immm",
      "spacegroup_number": 71,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.275524336941921e-15,
      "parent_symmetrization_rmsd_A": 0.4331070974736832,
      "parent_cell_rmsd_A": 0.0021364916779115393,
      "energy_eV": -213.505334295061,
      "reduced_polarization": [
        2.8781327000359665e-15,
        7.873406604740649e-16,
        1.3511130697490687e-15
      ],
      "cartesian_polarization_e_A2": [
        6.353086479690836e-17,
        2.0485030488294133e-17,
        1.8219692848733605e-17
      ],
      "ranking_score": 0.43364122039316766
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Imm2",
      "spacegroup_number": 44,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.6877048212404766e-05,
      "parent_symmetrization_rmsd_A": 0.028758508823599642,
      "parent_cell_rmsd_A": 0.019416652679311617,
      "energy_eV": -227.9434171632433,
      "reduced_polarization": [
        2.5266380161740374e-16,
        -9.249783297346303e-16,
        -0.4999831229517876
      ],
      "cartesian_polarization_e_A2": [
        4.181190451902827e-17,
        1.1735284792547489e-17,
        -0.006714920471428194
      ],
      "ranking_score": 0.5336464260898524
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.991689066731507e-05,
      "parent_symmetrization_rmsd_A": 0.06775421294304086,
      "parent_cell_rmsd_A": 0.053867345262627465,
      "energy_eV": -226.37898597994666,
      "reduced_polarization": [
        3.215664743687043e-15,
        0.49996701958638207,
        -2.2486673345259712e-05
      ],
      "cartesian_polarization_e_A2": [
        2.3559990071807158e-17,
        0.013010162013467587,
        -0.0001251867551617037
      ],
      "ranking_score": 0.5813008830400324
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.328151344675097e-05,
      "parent_symmetrization_rmsd_A": 0.05705165610018877,
      "parent_cell_rmsd_A": 0.041601800042416044,
      "energy_eV": -227.1385633624429,
      "reduced_polarization": [
        -0.5000067387982472,
        2.6212416585272536e-15,
        -5.285364957464984e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.011039719778912693,
        1.6714786060674443e-16,
        -9.71709707952117e-05
      ],
      "ranking_score": 0.5675586691376863
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 6.297902965918655e-05,
      "parent_symmetrization_rmsd_A": 0.07485135689377444,
      "parent_cell_rmsd_A": 0.0585170188333922,
      "energy_eV": -226.09913419495095,
      "reduced_polarization": [
        7.166764235287107e-16,
        0.4999788522905451,
        -0.5000593222771109
      ],
      "cartesian_polarization_e_A2": [
        5.082744783181324e-17,
        0.013111901092871584,
        -0.006842593640504436
      ],
      "ranking_score": 0.5896065696614409
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.494965560250642e-05,
      "parent_symmetrization_rmsd_A": 0.06525352221550001,
      "parent_cell_rmsd_A": 0.04729946477908131,
      "energy_eV": -226.8890394947549,
      "reduced_polarization": [
        -0.49997554353525914,
        -3.490015531899846e-15,
        -0.4999950637415928
      ],
      "cartesian_polarization_e_A2": [
        -0.01114777437050526,
        2.3530635876703192e-17,
        -0.006813084641438836
      ],
      "ranking_score": 0.5771282877214754
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00017567773952341452,
      "parent_symmetrization_rmsd_A": 0.08828680768385397,
      "parent_cell_rmsd_A": 0.06793789981789575,
      "energy_eV": -225.2080950106154,
      "reduced_polarization": [
        -0.5000205043301701,
        0.4999248382259845,
        -0.0001574577668302654
      ],
      "cartesian_polarization_e_A2": [
        -0.011042657154486511,
        0.013011335653356788,
        -0.00022304983465199434
      ],
      "ranking_score": 0.6056226381173747
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0001885565336222744,
      "parent_symmetrization_rmsd_A": 0.09487922006465287,
      "parent_cell_rmsd_A": 0.07262775711586533,
      "energy_eV": -225.01613341967348,
      "reduced_polarization": [
        -0.4999774402989526,
        0.4999347553809078,
        -0.5001754644292722
      ],
      "cartesian_polarization_e_A2": [
        -0.011150559151746307,
        0.013112919642276868,
        -0.006941645939820029
      ],
      "ranking_score": 0.6134132724108637
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "target_residual": 0.04870000735998039,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.0027815927244086405,
            "max_log_strain_component": 0.0005522800270725974,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.000552432561766,
              0.9998815611426073,
              0.9997158245581921
            ],
            "cell_volume_ratio": 1.0001496295213246,
            "cell_rmsd_from_input_A": 0.0021364916779115393
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.868565190067918e-15,
              -3.625202719281328e-15,
              -0.00010076653596583094
            ],
            "branch_aligned_reduced_polarization": [
              -1.868565190067918e-15,
              -3.625202719281328e-15,
              -0.00010076653596583094
            ],
            "target_residual": 0.00010076653596583094,
            "energy_eV": -228.2849939665416
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Immm",
        "spacegroup_number": 71,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.4669118491483384e-15,
        "parent_symmetrization_rmsd_A": 0.4331070561133806,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -213.53605977324105,
        "reduced_polarization": [
          -2.398053859093839e-15,
          3.6745172009100903e-16,
          4.471811643571084e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.295674680237815e-17,
          9.562922539558246e-18,
          6.027788212177757e-18
        ],
        "ranking_score": 0.4331070561133855
      },
      "branch_status": "sampled",
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -228.2881069961974,
          -227.4248722588372,
          -225.34412721549498,
          -222.56623699897122,
          -219.61785765233356,
          -216.9966042320743,
          -215.0523720346057,
          -213.90693836003817,
          -213.53605977324105
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.1330210852330135e-18,
            4.7470303777728544e-18,
            -0.0006564528063687445
          ],
          [
            1.4291755154544065e-17,
            -2.896348940355126e-18,
            0.009089717813660338
          ],
          [
            -1.664796343677971e-17,
            -2.6892648736331745e-17,
            0.01832149249335102
          ],
          [
            7.46647640911721e-17,
            -4.2040595748581746e-17,
            0.026568911205239874
          ],
          [
            -1.2476315986264145e-17,
            5.888856239822625e-17,
            0.03261654911339635
          ],
          [
            3.186675135810501e-17,
            3.8807257649265755e-17,
            0.0343179150117577
          ],
          [
            9.675904503279158e-17,
            3.983272740026196e-17,
            0.02931591476152165
          ],
          [
            8.289217989635559e-17,
            7.982845510112255e-17,
            0.01703299163613088
          ],
          [
            -7.288795128817474e-17,
            3.684415316953387e-17,
            5.83179469562329e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.112911242054697e-16,
            0.6743353370276494
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353048e-15,
            1.3592093911635132
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            1.9710574144686661
          ],
          [
            -5.649681958331948e-16,
            2.262770973769128e-15,
            2.4197111604506505
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            2.5459297263069707
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            2.1748482919101604
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            1.2636198824872185
          ],
          [
            -3.3006036703939277e-15,
            1.4157227982803701e-15,
            4.326410700714125e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.1129112420546972e-16,
            -0.3256646629723507
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353046e-15,
            -0.6407906088364868
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            -1.028942585531334
          ],
          [
            -5.649681958331946e-16,
            2.2627709737691274e-15,
            -0.5802888395493493
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            -0.45407027369302955
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            -0.8251517080898398
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            -0.7363801175127815
          ],
          [
            -3.300603670393928e-15,
            1.4157227982803701e-15,
            -0.9999999999999957
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.048700007359981534
          ],
          [
            6.661338147750939e-16,
            -1.1102230246251565e-16,
            -0.3256646629723507
          ],
          [
            -7.771561172376096e-16,
            -1.0547118733938987e-15,
            0.35920939116351325
          ],
          [
            3.3306690738754696e-15,
            -1.609823385706477e-15,
            -0.02894258553133411
          ],
          [
            -5.551115123125783e-16,
            2.220446049250313e-15,
            0.4197111604506507
          ],
          [
            1.4432899320127035e-15,
            1.4432899320127035e-15,
            -0.45407027369302955
          ],
          [
            4.3298697960381105e-15,
            1.5543122344752192e-15,
            0.17484829191016016
          ],
          [
            3.774758283725532e-15,
            3.1086244689504383e-15,
            0.26361988248721846
          ],
          [
            -3.2751579226442118e-15,
            1.4432899320127035e-15,
            4.3298697960381105e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -213.53605977324105,
          -213.90693836003814,
          -215.05237203460575,
          -216.99660423207436,
          -219.61785765233347,
          -222.56623699897122,
          -225.344127215495,
          -227.42487225883718,
          -228.2881069961974
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.845014788886216e-17,
            1.6645447438677777e-17,
            -5.361462411142023e-17
          ],
          [
            7.400811588136874e-17,
            8.020086058646436e-18,
            -0.017032991636130843
          ],
          [
            1.0290063711271728e-16,
            3.760380047101319e-19,
            -0.029315914761521678
          ],
          [
            2.5879664739309527e-17,
            5.505794199529682e-18,
            -0.03431791501175777
          ],
          [
            9.695217685920435e-18,
            4.18826558036851e-18,
            -0.032616549113396426
          ],
          [
            1.4948403364347442e-17,
            2.6853964625587946e-17,
            -0.026568911205239857
          ],
          [
            3.630878336559844e-18,
            8.239496547174167e-17,
            -0.018321492493351035
          ],
          [
            7.879778517640513e-18,
            1.0392779026307852e-16,
            -0.009089717813660234
          ],
          [
            1.236043689041649e-18,
            3.27045164019467e-17,
            0.0006564528063687848
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.552478036338138e-15,
            6.395950890248635e-16,
            -3.977487130068161e-15
          ],
          [
            3.351328369091026e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760463e-17,
            -2.174848291910162
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -2.5459297263069756
          ],
          [
            4.3903101286108947e-16,
            1.6093253765657604e-16,
            -2.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -1.9710574144686648
          ],
          [
            1.6441798888024866e-16,
            3.165995715660096e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -0.6743353370276417
          ],
          [
            5.597208132093571e-17,
            1.256658804557782e-15,
            0.04870000735998451
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.552478036338138e-15,
            6.395950890248635e-16,
            -1.000000000000004
          ],
          [
            3.3513283690910254e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760475e-17,
            -1.1748482919101622
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -1.5459297263069756
          ],
          [
            4.390310128610894e-16,
            1.6093253765657604e-16,
            -1.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -0.9710574144686648
          ],
          [
            1.644179888802486e-16,
            3.1659957156600957e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -1.6743353370276417
          ],
          [
            5.597208132093572e-17,
            1.256658804557782e-15,
            -1.9512999926400156
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.788363987704733e-15,
          2.6490427306563718e-15,
          0.04870000735999018
        ],
        "actual_opposite_endpoint_branch_residual": 9.061624714642027e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.112911242054697e-16,
            0.6743353370276494
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353048e-15,
            1.3592093911635132
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            1.9710574144686661
          ],
          [
            -5.649681958331948e-16,
            2.262770973769128e-15,
            2.4197111604506505
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            2.5459297263069707
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            2.1748482919101604
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            1.2636198824872185
          ],
          [
            -3.3006036703939277e-15,
            1.4157227982803701e-15,
            4.326410700714125e-15
          ],
          [
            3.351328369091026e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760463e-17,
            -2.174848291910162
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -2.5459297263069756
          ],
          [
            4.3903101286108947e-16,
            1.6093253765657604e-16,
            -2.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -1.9710574144686648
          ],
          [
            1.6441798888024866e-16,
            3.165995715660096e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -0.6743353370276417
          ],
          [
            5.597208132093571e-17,
            1.256658804557782e-15,
            0.04870000735998451
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.1129112420546972e-16,
            -0.3256646629723507
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353046e-15,
            -0.6407906088364868
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            -1.028942585531334
          ],
          [
            -5.649681958331946e-16,
            2.2627709737691274e-15,
            -0.5802888395493493
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            -0.45407027369302955
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            -0.8251517080898398
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            -0.7363801175127815
          ],
          [
            -3.300603670393928e-15,
            1.4157227982803701e-15,
            -0.9999999999999957
          ],
          [
            3.351328369091026e-15,
            3.0816880564878963e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760475e-17,
            -1.1748482919101622
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -1.5459297263069756
          ],
          [
            4.390310128610894e-16,
            1.6093253765657604e-16,
            -1.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -0.9710574144686648
          ],
          [
            1.644179888802486e-16,
            3.1659957156600957e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -1.6743353370276417
          ],
          [
            5.597208132093572e-17,
            1.256658804557782e-15,
            -1.9512999926400154
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.048700007359981534
          ],
          [
            6.661338147750939e-16,
            -1.1102230246251565e-16,
            -0.3256646629723507
          ],
          [
            -7.771561172376096e-16,
            -1.0547118733938987e-15,
            0.35920939116351325
          ],
          [
            3.3306690738754696e-15,
            -1.609823385706477e-15,
            -0.02894258553133411
          ],
          [
            -5.551115123125783e-16,
            2.220446049250313e-15,
            0.4197111604506507
          ],
          [
            1.4432899320127035e-15,
            1.4432899320127035e-15,
            -0.45407027369302955
          ],
          [
            4.3298697960381105e-15,
            1.5543122344752192e-15,
            0.17484829191016016
          ],
          [
            3.774758283725532e-15,
            3.1086244689504383e-15,
            0.26361988248721846
          ],
          [
            -3.2751579226442118e-15,
            1.4432899320127035e-15,
            4.3298697960381105e-15
          ],
          [
            3.3306690738754696e-15,
            3.3306690738754696e-16,
            -0.2636198824872156
          ],
          [
            4.6629367034256575e-15,
            0.0,
            -0.17484829191016216
          ],
          [
            1.2212453270876722e-15,
            2.220446049250313e-16,
            0.45407027369302444
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            -0.41971116045065626
          ],
          [
            6.661338147750939e-16,
            9.992007221626409e-16,
            0.02894258553133522
          ],
          [
            1.1102230246251565e-16,
            3.219646771412954e-15,
            -0.35920939116351436
          ],
          [
            3.3306690738754696e-16,
            3.9968028886505635e-15,
            0.3256646629723583
          ],
          [
            1.1102230246251565e-16,
            1.2212453270876722e-15,
            0.04870000735998459
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998037
            ],
            "target_residual": 0.45129999264001963,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.025776849822095396,
            "max_log_strain_component": 0.00511794526663483,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0026372822325655,
              1.0010982332741958,
              0.9948951291010988
            ],
            "cell_volume_ratio": 0.9986144568490599,
            "cell_rmsd_from_input_A": 0.019802757811120446
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.5568191667487566e-14,
              -1.0436757620063794e-14,
              -0.509449420192638
            ],
            "branch_aligned_reduced_polarization": [
              -1.5568191667487566e-14,
              -1.0436757620063794e-14,
              -0.509449420192638
            ],
            "target_residual": 0.009449420192637947,
            "energy_eV": -227.92873953038367,
            "max_atomic_step_A": 0.0005222296181922102,
            "max_log_strain_component": 9.976803648836518e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0025858052541083,
              1.0010768130473813,
              0.99499439278623
            ],
            "cell_volume_ratio": 0.9986414479502069,
            "cell_rmsd_from_input_A": 0.019416652679311617
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.5266380161740374e-16,
              -9.249783297346303e-16,
              -0.4999831229517876
            ],
            "branch_aligned_reduced_polarization": [
              2.5266380161740374e-16,
              -9.249783297346303e-16,
              -0.4999831229517876
            ],
            "target_residual": 1.6877048212404766e-05,
            "energy_eV": -227.9434171632433
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Imm2",
        "spacegroup_number": 44,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.6877048212404766e-05,
        "parent_symmetrization_rmsd_A": 0.028758508823599642,
        "parent_cell_rmsd_A": 0.019416652679311617,
        "energy_eV": -227.9434171632433,
        "reduced_polarization": [
          2.5266380161740374e-16,
          -9.249783297346303e-16,
          -0.4999831229517876
        ],
        "cartesian_polarization_e_A2": [
          4.181190451902827e-17,
          1.1735284792547489e-17,
          -0.006714920471428194
        ],
        "ranking_score": 0.5336464260898524
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.7256416629247826e-16,
              1.3877787807814457e-15,
              -0.04870000735998039
            ],
            "target_residual": 0.5023660923239752,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.06681747259402378,
            "max_log_strain_component": 0.009600304313112781,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.009871481930654,
              0.9997158245582198,
              0.9906546983208869
            ],
            "cell_volume_ratio": 1.0001496295213397,
            "cell_rmsd_from_input_A": 0.05391052187502405
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.828038706706158e-15,
              0.500765556492186,
              0.01955209901646969
            ],
            "branch_aligned_reduced_polarization": [
              4.828038706706158e-15,
              0.500765556492186,
              0.01955209901646969
            ],
            "target_residual": 0.019567080842388403,
            "energy_eV": -226.36623367579818,
            "max_atomic_step_A": 0.0011890726453489592,
            "max_log_strain_component": 0.00022441309705462144,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0097769425571865,
              0.9998312864757495,
              0.990572809981585
            ],
            "cell_volume_ratio": 1.0000888264614243,
            "cell_rmsd_from_input_A": 0.053867345262627465
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.215664743687043e-15,
              0.49996701958638207,
              -2.2486673345259712e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.215664743687043e-15,
              0.49996701958638207,
              -2.2486673345259712e-05
            ],
            "target_residual": 3.991689066731507e-05,
            "energy_eV": -226.37898597994666
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.991689066731507e-05,
        "parent_symmetrization_rmsd_A": 0.06775421294304086,
        "parent_cell_rmsd_A": 0.053867345262627465,
        "energy_eV": -226.37898597994666,
        "reduced_polarization": [
          3.215664743687043e-15,
          0.49996701958638207,
          -2.2486673345259712e-05
        ],
        "cartesian_polarization_e_A2": [
          2.3559990071807158e-17,
          0.013010162013467587,
          -0.0001251867551617037
        ],
        "ranking_score": 0.5813008830400324
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "target_residual": 0.5023660923239762,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.04703142132126793,
            "max_log_strain_component": 0.00876928130011561,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.008953123413065,
              0.999881561142616,
              0.9913920448043398
            ],
            "cell_volume_ratio": 1.0001496295213474,
            "cell_rmsd_from_input_A": 0.04179298655284559
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5031281603024819,
              -1.456680651638712e-15,
              0.023849983753334695
            ],
            "branch_aligned_reduced_polarization": [
              -0.5031281603024819,
              -1.456680651638712e-15,
              0.023849983753334695
            ],
            "target_residual": 0.024054253509771455,
            "energy_eV": -227.1152155005636,
            "max_atomic_step_A": 0.0013848776485648946,
            "max_log_strain_component": 0.0002679496907500472,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0088480750694935,
              0.9999390223688855,
              0.9913663332820537
            ],
            "cell_volume_ratio": 1.0000770309732363,
            "cell_rmsd_from_input_A": 0.041601800042416044
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000067387982472,
              2.6212416585272536e-15,
              -5.285364957464984e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000067387982472,
              2.6212416585272536e-15,
              -5.285364957464984e-05
            ],
            "target_residual": 5.328151344675097e-05,
            "energy_eV": -227.1385633624429
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.328151344675097e-05,
        "parent_symmetrization_rmsd_A": 0.05705165610018877,
        "parent_cell_rmsd_A": 0.041601800042416044,
        "energy_eV": -227.1385633624429,
        "reduced_polarization": [
          -0.5000067387982472,
          2.6212416585272536e-15,
          -5.285364957464984e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.011039719778912693,
          1.6714786060674443e-16,
          -9.71709707952117e-05
        ],
        "ranking_score": 0.5675586691376863
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.7256416629247826e-16,
              1.3877787807814457e-15,
              -0.04870000735998037
            ],
            "target_residual": 0.6735515446919266,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.0723615163769043,
            "max_log_strain_component": 0.009600304313118594,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0081133764231043,
              1.0026372822325935,
              0.9879719675678469
            ],
            "cell_volume_ratio": 0.9986144568490748,
            "cell_rmsd_from_input_A": 0.057245012801590694
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3289445236314713e-14,
              0.4900221982766149,
              -0.48803268246559384
            ],
            "branch_aligned_reduced_polarization": [
              -1.3289445236314713e-14,
              0.4900221982766149,
              -0.48803268246559384
            ],
            "target_residual": 0.015581181476399392,
            "energy_eV": -226.1907526961953,
            "max_atomic_step_A": 0.0016049371401973024,
            "max_log_strain_component": 0.0002062227047409415,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0082813288325347,
              1.0027115928708357,
              0.9876956567151787
            ],
            "cell_volume_ratio": 0.9985754970271157,
            "cell_rmsd_from_input_A": 0.0585170188333922
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.166764235287107e-16,
              0.4999788522905451,
              -0.5000593222771109
            ],
            "branch_aligned_reduced_polarization": [
              7.166764235287107e-16,
              0.4999788522905451,
              -0.5000593222771109
            ],
            "target_residual": 6.297902965918655e-05,
            "energy_eV": -226.09913419495095
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 6.297902965918655e-05,
        "parent_symmetrization_rmsd_A": 0.07485135689377444,
        "parent_cell_rmsd_A": 0.0585170188333922,
        "energy_eV": -226.09913419495095,
        "reduced_polarization": [
          7.166764235287107e-16,
          0.4999788522905451,
          -0.5000593222771109
        ],
        "cartesian_polarization_e_A2": [
          5.082744783181324e-17,
          0.013111901092871584,
          -0.006842593640504436
        ],
        "ranking_score": 0.5896065696614409
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              1.4098395246681691e-15,
              -0.04870000735998037
            ],
            "target_residual": 0.6735515446919274,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.05314134805456823,
            "max_log_strain_component": 0.008769281300109863,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0083804879858136,
              1.0010982332742047,
              0.9892287288708335
            ],
            "cell_volume_ratio": 0.9986144568490823,
            "cell_rmsd_from_input_A": 0.04620317865262639
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4897748909686615,
              -1.1598848433607582e-14,
              -0.4867595979833719
            ],
            "branch_aligned_reduced_polarization": [
              -0.4897748909686615,
              -1.1598848433607582e-14,
              -0.4867595979833719
            ],
            "target_residual": 0.01672904959239134,
            "energy_eV": -226.9494557464576,
            "max_atomic_step_A": 0.0012462165997500806,
            "max_log_strain_component": 0.00019465336439307,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0085700528095496,
              1.0011316920606892,
              0.9889679920612806
            ],
            "cell_volume_ratio": 0.9985722988701138,
            "cell_rmsd_from_input_A": 0.04729946477908131
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49997554353525914,
              -3.490015531899846e-15,
              -0.4999950637415928
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997554353525914,
              -3.490015531899846e-15,
              -0.4999950637415928
            ],
            "target_residual": 2.494965560250642e-05,
            "energy_eV": -226.8890394947549
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.494965560250642e-05,
        "parent_symmetrization_rmsd_A": 0.06525352221550001,
        "parent_cell_rmsd_A": 0.04729946477908131,
        "energy_eV": -226.8890394947549,
        "reduced_polarization": [
          -0.49997554353525914,
          -3.490015531899846e-15,
          -0.4999950637415928
        ],
        "cartesian_polarization_e_A2": [
          -0.01114777437050526,
          2.3530635876703192e-17,
          -0.006813084641438836
        ],
        "ranking_score": 0.5771282877214754
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              1.3877787807814457e-15,
              -0.04870000735998039
            ],
            "target_residual": 0.708781835769555,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.09030422790751101,
            "max_log_strain_component": 0.009600304313113225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0132746945832518,
              0.9997912376571952,
              0.9872529848482505
            ],
            "cell_volume_ratio": 1.000149629521362,
            "cell_rmsd_from_input_A": 0.06818800257643794
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5058043154324678,
              0.502187459100657,
              0.045004733218484874
            ],
            "branch_aligned_reduced_polarization": [
              -0.5058043154324678,
              0.502187459100657,
              0.045004733218484874
            ],
            "target_residual": 0.045430177932995454,
            "energy_eV": -225.13674752358534,
            "max_atomic_step_A": 0.0028091251233709875,
            "max_log_strain_component": 0.0005080441978283253,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0130568836976863,
              0.9999832407783439,
              0.9871397744865714
            ],
            "cell_volume_ratio": 1.000011984012025,
            "cell_rmsd_from_input_A": 0.06793789981789575
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000205043301701,
              0.4999248382259845,
              -0.0001574577668302654
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000205043301701,
              0.4999248382259845,
              -0.0001574577668302654
            ],
            "target_residual": 0.00017567773952341452,
            "energy_eV": -225.2080950106154
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00017567773952341452,
        "parent_symmetrization_rmsd_A": 0.08828680768385397,
        "parent_cell_rmsd_A": 0.06793789981789575,
        "energy_eV": -225.2080950106154,
        "reduced_polarization": [
          -0.5000205043301701,
          0.4999248382259845,
          -0.0001574577668302654
        ],
        "cartesian_polarization_e_A2": [
          -0.011042657154486511,
          0.013011335653356788,
          -0.00022304983465199434
        ],
        "ranking_score": 0.6056226381173747
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.7256416629247826e-16,
              1.4098395246681691e-15,
              -0.04870000735998039
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              1.3877787807814457e-15,
              -0.04870000735998037
            ],
            "target_residual": 0.8388514071972938,
            "energy_eV": -228.2881069961974,
            "max_atomic_step_A": 0.09432020269213483,
            "max_log_strain_component": 0.009600304313119038,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0119009597498976,
              1.0019124579083314,
              0.9849860152676629
            ],
            "cell_volume_ratio": 0.9986144568490977,
            "cell_rmsd_from_input_A": 0.07085718756460616
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49200880991822843,
              0.4913613666985418,
              -0.4635309106782
            ],
            "branch_aligned_reduced_polarization": [
              -0.49200880991822843,
              0.4913613666985418,
              -0.4635309106782
            ],
            "target_residual": 0.03832074608096107,
            "energy_eV": -225.15949807994562,
            "max_atomic_step_A": 0.002849499905158065,
            "max_log_strain_component": 0.0004175997551375792,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.763580920654891,
            "cell_principal_stretches": [
              1.0121010255606941,
              1.0020658361111732,
              0.9845291871379312
            ],
            "cell_volume_ratio": 0.9985014879288563,
            "cell_rmsd_from_input_A": 0.07262775711586533
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999774402989526,
              0.4999347553809078,
              -0.5001754644292722
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999774402989526,
              0.4999347553809078,
              -0.5001754644292722
            ],
            "target_residual": 0.0001885565336222744,
            "energy_eV": -225.01613341967348
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0001885565336222744,
        "parent_symmetrization_rmsd_A": 0.09487922006465287,
        "parent_cell_rmsd_A": 0.07262775711586533,
        "energy_eV": -225.01613341967348,
        "reduced_polarization": [
          -0.4999774402989526,
          0.4999347553809078,
          -0.5001754644292722
        ],
        "cartesian_polarization_e_A2": [
          -0.011150559151746307,
          0.013112919642276868,
          -0.006941645939820029
        ],
        "ranking_score": 0.6134132724108637
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29
        ],
        "endpoint_rmsd_A": 0.4331070561133806,
        "minimum_distance_A_by_image": [
          1.686288970086495,
          1.678901401347333,
          1.672472446294791,
          1.6541079218126802,
          1.630450961790199,
          1.6118110690847494,
          1.5983637783270985,
          1.5902408229996017,
          1.5875239350079866
        ],
        "minimum_distance_A": 1.5875239350079866,
        "minimum_distance_floor_A": 0.0,
        "geometry_valid": true,
        "parameters": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "cell_mode": "variable_cell",
        "cell_volume_A3_by_image": [
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904,
          359.28277761312904
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.3006036703939277e-15,
        1.4157227982803701e-15,
        4.326410700714125e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -228.2881069961974,
          -227.4248722588372,
          -225.34412721549498,
          -222.56623699897122,
          -219.61785765233356,
          -216.9966042320743,
          -215.0523720346057,
          -213.90693836003817,
          -213.53605977324105
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.1330210852330135e-18,
            4.7470303777728544e-18,
            -0.0006564528063687445
          ],
          [
            1.4291755154544065e-17,
            -2.896348940355126e-18,
            0.009089717813660338
          ],
          [
            -1.664796343677971e-17,
            -2.6892648736331745e-17,
            0.01832149249335102
          ],
          [
            7.46647640911721e-17,
            -4.2040595748581746e-17,
            0.026568911205239874
          ],
          [
            -1.2476315986264145e-17,
            5.888856239822625e-17,
            0.03261654911339635
          ],
          [
            3.186675135810501e-17,
            3.8807257649265755e-17,
            0.0343179150117577
          ],
          [
            9.675904503279158e-17,
            3.983272740026196e-17,
            0.02931591476152165
          ],
          [
            8.289217989635559e-17,
            7.982845510112255e-17,
            0.01703299163613088
          ],
          [
            -7.288795128817474e-17,
            3.684415316953387e-17,
            5.83179469562329e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.112911242054697e-16,
            0.6743353370276494
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353048e-15,
            1.3592093911635132
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            1.9710574144686661
          ],
          [
            -5.649681958331948e-16,
            2.262770973769128e-15,
            2.4197111604506505
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            2.5459297263069707
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            2.1748482919101604
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            1.2636198824872185
          ],
          [
            -3.3006036703939277e-15,
            1.4157227982803701e-15,
            4.326410700714125e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.1129112420546972e-16,
            -0.3256646629723507
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353046e-15,
            -0.6407906088364868
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            -1.028942585531334
          ],
          [
            -5.649681958331946e-16,
            2.2627709737691274e-15,
            -0.5802888395493493
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            -0.45407027369302955
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            -0.8251517080898398
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            -0.7363801175127815
          ],
          [
            -3.300603670393928e-15,
            1.4157227982803701e-15,
            -0.9999999999999957
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.048700007359981534
          ],
          [
            6.661338147750939e-16,
            -1.1102230246251565e-16,
            -0.3256646629723507
          ],
          [
            -7.771561172376096e-16,
            -1.0547118733938987e-15,
            0.35920939116351325
          ],
          [
            3.3306690738754696e-15,
            -1.609823385706477e-15,
            -0.02894258553133411
          ],
          [
            -5.551115123125783e-16,
            2.220446049250313e-15,
            0.4197111604506507
          ],
          [
            1.4432899320127035e-15,
            1.4432899320127035e-15,
            -0.45407027369302955
          ],
          [
            4.3298697960381105e-15,
            1.5543122344752192e-15,
            0.17484829191016016
          ],
          [
            3.774758283725532e-15,
            3.1086244689504383e-15,
            0.26361988248721846
          ],
          [
            -3.2751579226442118e-15,
            1.4432899320127035e-15,
            4.3298697960381105e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -213.53605977324105,
          -213.90693836003814,
          -215.05237203460575,
          -216.99660423207436,
          -219.61785765233347,
          -222.56623699897122,
          -225.344127215495,
          -227.42487225883718,
          -228.2881069961974
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.845014788886216e-17,
            1.6645447438677777e-17,
            -5.361462411142023e-17
          ],
          [
            7.400811588136874e-17,
            8.020086058646436e-18,
            -0.017032991636130843
          ],
          [
            1.0290063711271728e-16,
            3.760380047101319e-19,
            -0.029315914761521678
          ],
          [
            2.5879664739309527e-17,
            5.505794199529682e-18,
            -0.03431791501175777
          ],
          [
            9.695217685920435e-18,
            4.18826558036851e-18,
            -0.032616549113396426
          ],
          [
            1.4948403364347442e-17,
            2.6853964625587946e-17,
            -0.026568911205239857
          ],
          [
            3.630878336559844e-18,
            8.239496547174167e-17,
            -0.018321492493351035
          ],
          [
            7.879778517640513e-18,
            1.0392779026307852e-16,
            -0.009089717813660234
          ],
          [
            1.236043689041649e-18,
            3.27045164019467e-17,
            0.0006564528063687848
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.552478036338138e-15,
            6.395950890248635e-16,
            -3.977487130068161e-15
          ],
          [
            3.351328369091026e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760463e-17,
            -2.174848291910162
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -2.5459297263069756
          ],
          [
            4.3903101286108947e-16,
            1.6093253765657604e-16,
            -2.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -1.9710574144686648
          ],
          [
            1.6441798888024866e-16,
            3.165995715660096e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -0.6743353370276417
          ],
          [
            5.597208132093571e-17,
            1.256658804557782e-15,
            0.04870000735998451
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.552478036338138e-15,
            6.395950890248635e-16,
            -1.000000000000004
          ],
          [
            3.3513283690910254e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760475e-17,
            -1.1748482919101622
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -1.5459297263069756
          ],
          [
            4.390310128610894e-16,
            1.6093253765657604e-16,
            -1.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -0.9710574144686648
          ],
          [
            1.644179888802486e-16,
            3.1659957156600957e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -1.6743353370276417
          ],
          [
            5.597208132093572e-17,
            1.256658804557782e-15,
            -1.9512999926400156
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.788363987704733e-15,
          2.6490427306563718e-15,
          0.04870000735999018
        ],
        "actual_opposite_endpoint_branch_residual": 9.061624714642027e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.112911242054697e-16,
            0.6743353370276494
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353048e-15,
            1.3592093911635132
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            1.9710574144686661
          ],
          [
            -5.649681958331948e-16,
            2.262770973769128e-15,
            2.4197111604506505
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            2.5459297263069707
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            2.1748482919101604
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            1.2636198824872185
          ],
          [
            -3.3006036703939277e-15,
            1.4157227982803701e-15,
            4.326410700714125e-15
          ],
          [
            3.351328369091026e-15,
            3.0816880564878953e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760463e-17,
            -2.174848291910162
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -2.5459297263069756
          ],
          [
            4.3903101286108947e-16,
            1.6093253765657604e-16,
            -2.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -1.9710574144686648
          ],
          [
            1.6441798888024866e-16,
            3.165995715660096e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -0.6743353370276417
          ],
          [
            5.597208132093571e-17,
            1.256658804557782e-15,
            0.04870000735998451
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8715664691687873e-16,
            1.8240286590436872e-16,
            -0.04870000735998152
          ],
          [
            6.47177190273319e-16,
            -1.1129112420546972e-16,
            -0.3256646629723507
          ],
          [
            -7.538739702913529e-16,
            -1.0333399643353046e-15,
            -0.6407906088364868
          ],
          [
            3.381063537292772e-15,
            -1.6153941598465287e-15,
            -1.028942585531334
          ],
          [
            -5.649681958331946e-16,
            2.2627709737691274e-15,
            -0.5802888395493493
          ],
          [
            1.4430302215553734e-15,
            1.4911543533109486e-15,
            -0.45407027369302955
          ],
          [
            4.3815644909044986e-15,
            1.5305576447572748e-15,
            -0.8251517080898398
          ],
          [
            3.753627703585251e-15,
            3.0673785150695567e-15,
            -0.7363801175127815
          ],
          [
            -3.300603670393928e-15,
            1.4157227982803701e-15,
            -0.9999999999999957
          ],
          [
            3.351328369091026e-15,
            3.0816880564878963e-16,
            -1.2636198824872156
          ],
          [
            4.659675769967897e-15,
            1.4449119615760475e-17,
            -1.1748482919101622
          ],
          [
            1.1719154526570913e-15,
            2.115580818223106e-16,
            -1.5459297263069756
          ],
          [
            4.390310128610894e-16,
            1.6093253765657604e-16,
            -1.4197111604506563
          ],
          [
            6.769123584750662e-16,
            1.0318535418557542e-15,
            -0.9710574144686648
          ],
          [
            1.644179888802486e-16,
            3.1659957156600957e-15,
            -1.3592093911635144
          ],
          [
            3.5682201842096516e-16,
            3.99338645058082e-15,
            -1.6743353370276417
          ],
          [
            5.597208132093572e-17,
            1.256658804557782e-15,
            -1.9512999926400154
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.220446049250313e-16,
            2.220446049250313e-16,
            -0.048700007359981534
          ],
          [
            6.661338147750939e-16,
            -1.1102230246251565e-16,
            -0.3256646629723507
          ],
          [
            -7.771561172376096e-16,
            -1.0547118733938987e-15,
            0.35920939116351325
          ],
          [
            3.3306690738754696e-15,
            -1.609823385706477e-15,
            -0.02894258553133411
          ],
          [
            -5.551115123125783e-16,
            2.220446049250313e-15,
            0.4197111604506507
          ],
          [
            1.4432899320127035e-15,
            1.4432899320127035e-15,
            -0.45407027369302955
          ],
          [
            4.3298697960381105e-15,
            1.5543122344752192e-15,
            0.17484829191016016
          ],
          [
            3.774758283725532e-15,
            3.1086244689504383e-15,
            0.26361988248721846
          ],
          [
            -3.2751579226442118e-15,
            1.4432899320127035e-15,
            4.3298697960381105e-15
          ],
          [
            3.3306690738754696e-15,
            3.3306690738754696e-16,
            -0.2636198824872156
          ],
          [
            4.6629367034256575e-15,
            0.0,
            -0.17484829191016216
          ],
          [
            1.2212453270876722e-15,
            2.220446049250313e-16,
            0.45407027369302444
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            -0.41971116045065626
          ],
          [
            6.661338147750939e-16,
            9.992007221626409e-16,
            0.02894258553133522
          ],
          [
            1.1102230246251565e-16,
            3.219646771412954e-15,
            -0.35920939116351436
          ],
          [
            3.3306690738754696e-16,
            3.9968028886505635e-15,
            0.3256646629723583
          ],
          [
            1.1102230246251565e-16,
            1.2212453270876722e-15,
            0.04870000735998459
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Immm",
        "spacegroup_number": 71,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.4669118491483384e-15,
        "parent_symmetrization_rmsd_A": 0.4331070561133806,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -213.53605977324105,
        "reduced_polarization": [
          -2.398053859093839e-15,
          3.6745172009100903e-16,
          4.471811643571084e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.295674680237815e-17,
          9.562922539558246e-18,
          6.027788212177757e-18
        ],
        "ranking_score": 0.4331070561133855
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 48,
      "full_response": 16,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 41,
      "energy_polarization": 32
    },
    "elapsed_seconds": 594.0402371289674
  }
}
